We have studied the mesoscopic shape fluctuations in aligned multilamellar stacks of 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine bilayers using the neutron spin-echo technique. The corresponding in plane dispersion relation tau-1(q//) at different temperatures in the gel (ripple, Pbeta') and the fluid (Lalpha) phase of this model system has been determined. Two relaxation processes, one at about 10 ns and a second, slower process at about 100 ns can be quantified. The dispersion relation in the fluid phase is fitted to a smectic hydrodynamic theory, with a correction for finite qz resolution. We extract values for the bilayer bending rigidity kappa, the compressional modulus of the stacks B, and the effective sliding viscosity eta3. The softening of a mode which can be associated with the formation of the ripple structure is observed close to the main phase transition.